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Math Expression Simplifier

Tool/Simplifier of math expressions. Simplification is a mathematical process aiming to rewrite an expression with the minimal number of items and variables.

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Math Expression Simplifier -

Tag(s) : Symbolic Computation

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# Math Expression Simplifier

## Boolean Expression Simplifier

### What is a simplification in mathematics? (Definition)

Simplification of a mathematical calculation refers to the process of reducing a mathematical expression to a more concise or explicit form, while preserving its equivalence.

The simplification modify the writing of a mathematical expression (in a more complex original format) towards a simplified format, facilitating reading or the continuation of calculations.

The expression to rewrite/simplify can be literal (formal, with letters and/or numbers).

### How to simplify a math expression?

To simplify an equation, or an algebraic calculation, dCode simplifier can perform various operations (such as the reduction of fractions, factorization, the use of remarkable identities, the cancellation of equivalent terms, or the simplification of roots) on the elements which compose it in order to reduce the mathematical expression in a simplified form.

Example: Simplification of expression: $$\frac{x^2-4}{\frac{(x-2) \left(x^2+4 x+4\right)}{x^2-x-6}} = x-3$$

Example: Expression factorization: $5x+5 = 5(x+1)$

### How to simplify a formula with remarkable identities?

To simplify a formula with notable identities, identify the relevant identities for the given expression and then apply them.

The remarkable identities allow a factorization of the mathematical expression and thus a simplification of its writing.

Example: $(x-1)(x+1) = x^2-1$

### How to simplify fractions to irreducible form?

dCode calculator create irreducible fractions (see gcd) and reduce them to the same denominator (see lcm).

Example: $\frac{15}{8} - \frac{2}{3} = \frac{29}{24}$

### How to simplify logarithms or exponentials?

To simplify expressions with exponentials or logarithms, use properties of exponentials or logarithms to combine/extract similar terms.

Example: $a^m \cdot a^n = a^{m + n}$

Example: $\log_a(bc) = \log_a(b) + \log_a(c)$

### How to simplify trigonometric expressions?

Simplifying trigonometric expressions consists of using trigonometric identities, to transform the equation into a more manageable form.

Example: $\sin^2(x) + \cos^2(x) = 1$ or $\sin(2a) = 2\sin(a)\cos(a)$

### How to simplify radix (roots) expression?

To simplify a root, look for square factors in the radicand and then extract them from the root.

dCode simplifies writing with radicals (nth root). Square roots can be indicated with the sqrt() function.

Example: $\sqrt{8}+\sqrt{2} = 3\sqrt{2}$

### How to simplify a mathematical equation?

To simplify a mathematical equation, the user can perform simplification operations on both sides of the equation to maintain equivalence.

NB: Simplifying is not solving, solving an equation aims to find the values of the unknown variable which satisfy the equation.

## Source code

dCode retains ownership of the "Math Expression Simplifier" source code. Except explicit open source licence (indicated Creative Commons / free), the "Math Expression Simplifier" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Math Expression Simplifier" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Math Expression Simplifier" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
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Math Expression Simplifier on dCode.fr [online website], retrieved on 2024-08-13, https://www.dcode.fr/math-simplification

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